The Wales No.8 was selected among the replacements in the Dragons 33-13 defeat to Munster last week but did not feature off the bench after hurting his ankle in the warm-up.
Faletau was already carrying a dead leg but he has made a full recovery and is certain to feature against the Scottish side.
“Toby had a dead leg leading into that game and didn’t train for most of the week,” said Dragons head coach Darren Edwards.
“Lewis Evans and Toby weren’t part of our preparations so we felt it wasn’t fair to pick them ahead of the players who had stepped in.
“As it was, Tom Brown at No.8, did really well and Jevon Groves at flanker had an excellent game.
“But Toby is fully recovered and will play against Edinburgh. With Lewis also back, our team will take on a different dimension this week.”
The Dragons will hold a shootout to decide who takes on the kicking duties in Friday’s RaboDirect PRO12 clash.
Tom Prydie was handed the responsibility following his Wales Under-20s heroics at the Junior World Championship.
But he has hit a blip on his radar and been off form from the tee in the recent defeats to Cardiff Blues and Munster.
That has led to Edwards reassessing his kicking options and he has revealed the best marksman in training this week will get the opportunity to boot the Dragons woes into touch.
“It’s tempting to flick a coin for it!” added Edwards.
“But the guy that steps up in the two sessions this week will get the kicking duties.
“These are young guys and it’s good to challenge them and take them out of their comfort zone.
“Lewis Robling has been our best kicker on the training ground and I was pleased that he showed plenty of confidence to put over two kicks when he took over against Munster. He was determined and showed great mental toughness.”
Dragons squad: D Evans, T Prydie, W Harries, A Hughes, A Tuilagi, P Leach, A Smith, L Robling, Steffan Jones, J Evans, L Davies, P Price, A Coundley, Steve Jones, S Parry, D Way, N Buck, I Nimmo, A Jones, H Stoddart, L Evans, T Faletau, T Brown, D Lydiate, J Groves.
